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A343683
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Primes p1 such that the sum of 9 consecutive primes, p1+p2+p3+p4+p5+p6+p7+p8+p9, and the three sums (p1+p2+p3), (p4+p5+p6), (p7+p8+p9) are all prime numbers.
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0
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29, 83, 389, 1151, 2293, 2521, 2699, 2753, 4831, 7121, 9857, 12409, 13679, 24439, 25943, 36083, 43201, 47317, 49037, 49069, 49109, 51829, 51859, 53717, 61471, 64091, 68449, 70271, 77047, 87337, 87911, 90709, 111109, 113173, 114577, 117577, 117889, 118051, 128549, 134837, 149533, 172489
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OFFSET
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1,1
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LINKS
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EXAMPLE
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n=1, p1=29:
29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 = 401,
29 + 31 + 37 = 97, 41 + 43 + 47 = 131, 53 + 59 + 61 = 173, all primes.
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MATHEMATICA
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Select[Prime@Range@10000, And@@PrimeQ[Flatten@{Total[s=NextPrime[#, 0~Range~8]], Total/@Partition[s, 3]}]&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)
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CROSSREFS
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Cf. A082251 (primes that are the sum of 9 consecutive primes).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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